Question

A soap bubble in vacuum has a radius of 3 cm and another soap bubble in vacuum has a radius of 4 cm. If the two bubble coalesce under isothermal condition, then the radius of the new bubble is :-

• A. 2.3 cm
• B. 4.5 cm
• C. 5 cm
• D. 7 cm

Answer 1

The correct option is C 5 cm

Since, it is given that the 2 bubbles join in isothermal conditions, therefore we can make use of the Boyle's law.

$P_1{V}_1+P_2{V}_2=P_3{V}_3$

For any radius of bubble. the product PV will be,

$\frac{4T}{r}\times 4/3\pi r^3$

Therefore, the product PV $\propto r^2$

Hence, substituting the values in the equation,

$3^2+4^2=R^2$

Applying, Pythagorus Theorem, R = 5 cm